Iterative Double Laplacian-Scaled Low-Rank Optimization for Under-Sampled and Noisy Signal Recovery
Iterative Double Laplacian-Scaled Low-Rank Optimization for Under-Sampled and Noisy Signal Recovery
复制标题
用于欠采样和噪声信号恢复的迭代双拉普拉斯尺度低阶优化
DOI：
10.1109/tgrs.2019.2925376
复制
发表时间：
2019
影响因子：
8.2
通讯作者：
Chen Yangkang
中科院分区：
文献类型：
--
作者：
Zhao Qiang;Du Qizhen;Sun Wenhan;Chen Yangkang
从欠采样和不稳定噪声污染的地震数据中恢复信号确实是一项具有挑战性的任务，因为它很难同时建模不稳定的噪声和丢失的信号。假设记录的数据是低秩和稀疏分量的叠加，许多相关的工作已经报道使用混合秩稀疏约束。这些已发表的工作通常使用经验和全局阈值来检测秩和不稳定的噪声，这通常不能很好地表征变化的稀疏性，并且在它们的非平稳分布的情况下容易导致有偏估计。我们提出了一种迭代双拉普拉斯尺度低秩优化自适应选择的稀疏性和秩正则化参数的鲁棒信号恢复。与已有的全局阈值方法相比，该方法采用Laplacian尺度混合（Laplacian scaled mixture）方法，即Laplacian变量与Gamma变量相乘的混合方法，对噪声的稀疏性和信号的低秩特征进行局部建模。然后，利用期望最大化（EM）算法将Laplacian尺度混合问题转化为局部加权极小化问题.在EM求解器中出现的加权系数提供了一个可变的约束，以局部解决秩和不稳定的噪声，因此，它们的正则化参数可以动态地反映这些系数的不同重要性。我们测试了所提出的方法的有效性，使用欠采样的合成和现场数据，被不稳定的噪声破坏，并使用其他国家的最先进的方法作为比较。结果表明，该方法可以对信号和不稳定噪声进行更准确的估计。
Recovering signal from under-sampled and erratic noise-corrupted seismic data is indeed a challenging task because of its difficulty in simultaneous modeling of erratic noise and missing signal. Assuming that the recorded data are the superposition of low-rank and sparse components, many related works have been reported using a hybrid rank-sparsity constraint. Those published works typically detect the rank and erratic noise using empirical and global thresholds, which often fail to well characterize the varying sparsity and easily cause biased estimation in case of their nonstationary distribution. We propose an iterative double Laplacian-scaled low-rank optimization to adaptively select the sparsity and rank regularizer parameters for robust signal recovery. Comparing with the published approaches with global threshold, Laplacian-scaled mixture, which is obtained by multiplying Laplacian variable with a Gamma variable, is used to locally model the sparsity of erratic noise and the low-rank feature of signal. Then, the expectation–maximization (EM) algorithm is used to transform the Laplacian-scaled mixture problem into a localized reweighted $\ell _{1}$ minimization scheme. The weighted coefficient appearing in its EM solver provides a variable constraint to locally address the rank and erratic noise, and hence, their regularizer parameters can dynamically reflect the different importance of those coefficients. We tested the effectiveness of the proposed method using under-sampled synthetic and field data that are corrupted by erratic noise and used other state-of-the-art methods as comparisons. The results showed that more exact estimations of the signal and erratic noise can be obtained using the proposed method.